Suppressing van der Waals driven rupture through shear

2010 ◽  
Vol 661 ◽  
pp. 522-539 ◽  
Author(s):  
M. J. DAVIS ◽  
M. B. GRATTON ◽  
S. H. DAVIS
Keyword(s):  
Free Surface ◽  
Wind Shear ◽  
Capillary Wave ◽  
Van Der Waals ◽  
Three Dimensional ◽  
Angular Speed ◽  
Critical Value ◽  
Finite Amplitude ◽  
Two Dimensions ◽  
Sivashinsky Equation

An ultra-thin viscous film on a substrate is susceptible to rupture instabilities driven by van der Waals attractions. When a unidirectional ‘wind’ shear τ is applied to the free surface, the rupture instability in two dimensions is suppressed when τ exceeds a critical value τc and is replaced by a permanent finite-amplitude structure, an intermolecular-capillary wave, that travels at approximately the speed of the surface. For small amplitudes, the wave is governed by the Kuramoto–Sivashinsky equation. If three-dimensional disturbances are allowed, the shear is decoupled from disturbances perpendicular to the flow, and line rupture would occur. In this case, replacing the unidirectional shear with a shear whose direction rotates with angular speed, , suppresses the rupture if τ ≳ 2τc. For the most dangerous wavenumber, τc ≈ 10−2 dyn cm−2 at ≈ 1 rad s−1 for a film with physical properties similar to water at a thickness of 100 nm.

Two- and Three-Dimensional EBSD Measurement of Dislocation Density in Deformed Structures

2010 ◽  
Vol 160 ◽  
pp. 17-22 ◽  
Author(s):  
David P. Field ◽  
Colin C. Merriman ◽  
Ioannis N. Mastorakos
Keyword(s):  
Free Surface ◽  
Dislocation Density ◽  
Bulk Material ◽  
Ion Beam ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Dislocation Dynamics ◽  
Three Dimensions ◽  
Lattice Curvature ◽  
Orientation Data

Electron backscatter diffraction (EBSD) techniques have been used to measure the dislocation density tensor for various materials. Orientation data are typically obtained over a planar array of measurement positions and the minimum dislocation content required to produce the observed lattice curvature is calculated as the geometrically necessary (or excess) dislocation density. The present work shows a comparison of measurements in two-dimensions and three-dimensions using a dual beam instrument (focused ion beam, electron beam) to obtain the data. The two-dimensional estimate is obviously lower than that obtained from three-dimensional data since the 2D analysis necessarily assumes that the third dimension has no curvature in the lattice. Effects of the free-surface on EBSD measurements are discussed in conjunction with comparisons against X-ray microdiffraction experiments and a discrete dislocation dynamics model. It is observed that the EBSD measurements are sensitive to free-surface effects that may yield dislocation density observations that are not consistent with that of the bulk material.

Preferred pattern of convection in a porous layer with a spatially non-uniform boundary temperature

1993 ◽  
Vol 246 ◽  
pp. 529-543 ◽  
Author(s):  
D. N. Riahi
Keyword(s):  
Porous Layer ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Critical Value ◽  
Finite Amplitude ◽  
Surprising Result ◽  
Dimensional Solution ◽  
Boundary Temperature ◽  
Steady Solutions ◽  
The One

The problem of finite-amplitude thermal convection in a porous layer between two horizontal walls with different mean temperatures is considered when spatially non-uniform temperature with amplitude L* is prescribed at the lower wall. The nonlinear problem of three-dimensional convection for values of the Rayleigh number close to the classical critical value is solved by using a perturbation technique. Two cases are considered: the wavelength γ(b)n of the nth mode of the modulation is equal to or not equal to the critical wavelength γc for the onset of classical convection. The preferred mode of convection is determined by a stability analysis in which arbitrary infinitesimal disturbances are superimposed on the steady solutions. The most surprising results for the case γ(b)n = γc for all n are that regular or non-regular solutions in the form of multi-modal pattern convection can become preferred in some range of L*, provided the wave vectors of such pattern are contained in the set of wave vectors representing the spatially non-uniform boundary temperature. There can be critical value(s) L*c of L* below which the preferred flow pattern is different from the one for L* > L*c. The most surprising result for the case γ(b)n ≠ γc and γ(b)n ≡ γ(b) for all n is that some three-dimensional solution in the form of multi-modal convection can be preferred, even if the boundary modulation is one-dimensional, provided that the wavelength of the modulation is not too small. Here γ(b) is a constant independent of n.

Studying the Impact of Unstructured Mesh Adaptation on Free Surface Flow Simulations

2009 ◽  
Author(s):  
Olivier Allain ◽  
Damien Gue´gan ◽  
Fre´de´ric Alauzet
Keyword(s):  
Free Surface ◽  
Message Passing ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Two Dimensions ◽  
Surface Flow ◽  
Mesh Adaptation ◽  
Message Passing Algorithm ◽  
Dimensional Simulation ◽  
The Impact

Engineering offshore problems require a continuous progress in the simulation of systems coupling structures and fluids with interfaces. The needs concern complex interface motions and fluid-structure interaction with slamming. The proposed methodology combines, in a parallel message passing algorithm, a level set based interface tracking, a standard finite element projection method on unstructured meshes and a dynamic mesh adaptation process for time dependent problems. This numerical method is applied to the study of a wedge impacting a free surface in two dimensions [1, 2] and the three-dimensional simulation of a breaking water column which impacts an obstacle [3] for which experimental results are available.

scholarly journals Enhanced Energy Dissipation by Parasitic Capillaries on Short Gravity–Capillary Waves

2010 ◽  
Vol 40 (11) ◽  
pp. 2435-2450 ◽  
Author(s):  
Wu-ting Tsai ◽  
Li-ping Hung
Keyword(s):  
Energy Dissipation ◽  
Dissipation Rate ◽  
Capillary Wave ◽  
Wave Train ◽  
Three Dimensional ◽  
Local Maximum ◽  
Finite Amplitude ◽  
Capillary Waves ◽  
Carrier Wave ◽  
Order Of Magnitude

Abstract The increased energy dissipation caused by the formation of parasitic capillary wavelets on moderately short, steep gravity–capillary waves is studied numerically. This study focuses on understanding the mechanism leading to dissipation enhancement and on exploring the possible correlation between the enhanced dissipation rate and the characteristic parameters of the parasitic capillaries. The interaction between the parasitic capillary wave train and the underlying dominant flow of the carrier wave induces strong vortex shedding and imposes large straining immediately underneath the troughs of the capillary ripples. These localized strains are very effective in dissipating energy of the carrier gravity–capillary wave. The attenuation rate of the carrier wave can increase by more than one order of magnitude in the presence of capillary wavelets. Systematic simulations for various carrier wavelengths and steepnesses reveal that the enhanced dissipation rate can be quantified well by a simple parameter: the average of all the difference between the local maximum and minimum slopes along the entire carrier wave surface, which is equivalent to the mean slope of the parasitic capillary wave train. The enhanced dissipation rate increases approximately linearly with the carrier gravity–capillary wavenumber for a given mean slope of the capillary wave train. The increased energy dissipation caused by the formation of parasitic capillaries is also found to significantly impact on the characteristics of three-dimensional instabilities of finite-amplitude, uniform gravity–capillary waves.

THREE-DIMENSIONAL QUANTUM GRAVITY AS DYNAMICAL TRIANGULATION

1991 ◽  
Vol 06 (20) ◽  
pp. 1863-1884 ◽  
Author(s):  
M. E. AGISHTEIN ◽  
A. A. MIGDAL
Keyword(s):  
Quantum Gravity ◽  
Three Dimensional ◽  
Critical Value ◽  
Two Dimensions ◽  
Geodesic Sphere ◽  
Closed Universe ◽  
3 Dimensional ◽  
Average Curvature ◽  
Dynamical Triangulation ◽  
The Universe

The dynamical triangulation model of 3-dimensional Quantum Gravity is defined and studied. We propose two different algorithms for numerical simulations, leading to consistent results. One is the 3-dimensional generalization of the bonds flip, another is more sophisticated algorithm, based on Schwinger–Dyson equations. We found such care necessary, because our results appear to be quite unexpected. We simulated up to 60000 tetrahedra and observed none of the feared pathologies like factorial growth of the partition function with volume, or collapse to the branched polymer phase. The volume of the Universe grows exponentially when the bare cosmological constant λ approaches the critical value λ c from above, but the closed Universe exists and has peculiar continuum limit. The Universe compressibility diverges as (λ − λ c )−2 and the bare Newton constant linearly approaches negative critical value as λ goes to λ c , provided the average curvature is kept at zero. The fractal properties turned out to be the same, as in two dimensions, namely the effective Hausdorff dimension grows logarithmically with the size of the test geodesic sphere.

THREE-DIMENSIONAL WAVE-FREE POTENTIALS IN THE THEORY OF WATER WAVES

2013 ◽  
Vol 55 (2) ◽  
pp. 175-195 ◽  
Author(s):  
HARPREET DHILLON ◽  
B. N. MANDAL
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Surface Condition ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Finite Depth ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Thin Elastic Plate ◽  
Linearized Theory

AbstractProblems of wave interaction with a body with arbitrary shape floating or submerged in water are of immense importance in the literature on the linearized theory of water waves. Wave-free potentials are used to construct solutions to these problems involving bodies with circular geometry, such as a submerged or half-immersed long horizontal circular cylinder (in two dimensions) or sphere (in three dimensions). These are singular solutions of Laplace’s equation satisfying the free surface condition and decaying rapidly away from the point of singularity. Wave-free potentials in two and three dimensions for infinitely deep water as well as water of uniform finite depth with a free surface are known in the literature. The method of constructing wave-free potentials in three dimensions is presented here in a systematic manner, neglecting or taking into account the effect of surface tension at the free surface or for water with an ice cover modelled as a thin elastic plate floating on the water. The forms of the wave motion at the upper surface (free surface or ice-covered surface) related to these wave-free potentials are depicted graphically in a number of figures for all the cases considered.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

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